Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 203
... eigenvalue equation Lf = λf ̧ ( 14.3 ) and its associated boundary conditions , and there also exists a nontrivial ... EIGENVALUES 203 A Simple Solution Nondegenerate Eigenvalues.
... eigenvalue equation Lf = λf ̧ ( 14.3 ) and its associated boundary conditions , and there also exists a nontrivial ... EIGENVALUES 203 A Simple Solution Nondegenerate Eigenvalues.
Página 227
... eigenvalue of and its eigencolumn have indeed been found . The iteration method of Cayley - Sylvester as described ... eigenvalue and its eigen- column are determined , whereas in many problems it is the lowest eigen- value and its ...
... eigenvalue of and its eigencolumn have indeed been found . The iteration method of Cayley - Sylvester as described ... eigenvalue and its eigen- column are determined , whereas in many problems it is the lowest eigen- value and its ...
Página 228
... eigenvalue of L and its eigencolumn . If the matrix operator L has an inverse the eigenvalue problem ( 16.1 ) may be replaced by the problem L ̄1y = λ ̃1y ( 16.8 ) Clearly , the largest eigenvalue of -1 to which the iteration method con ...
... eigenvalue of L and its eigencolumn . If the matrix operator L has an inverse the eigenvalue problem ( 16.1 ) may be replaced by the problem L ̄1y = λ ̃1y ( 16.8 ) Clearly , the largest eigenvalue of -1 to which the iteration method con ...
Contenido
34 | 12 |
Solution for Diagonalizable Matrices | 21 |
The Evaluation of a Function of a Matrix for an Arbitrary Matrix | 38 |
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approximation arbitrary ax² basis Bessel functions boundary conditions Chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal differential equation Dirac notation domain eigencolumns eigenfunctions eigenvectors elements evaluate expansion F₁ finite number follows formula Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplacian linear operator linearly independent lowest eigenvalue Mathematical matrix McGraw-Hill Book Company method multiplication nonsingular normal number of degrees obtained orthonormality conditions Physics problem relations representation result Ritz method scattering sinh solution solve spherical spherical harmonics string Substitution theorem transform trial functions vanish variable vector space Verify w₁ wave write written x₁ Y₁ yields York zero ηπχ ди ду дх